With machine tools, manipulating devices and robots, it happens that the driven components (i.e., adjusting elements) are not arranged at right angles to one another. To be operated, such machines require a so-called kinematic coordinate transformation which converts spatial coordinates (as a rule, Cartesian coordinates, in individual cases, also cylindrical or spherical coordinates) into desired values for the machine axes. In these machines, the accuracy of positioning is a function of a multiplicity of factors.
Thus, in particular the parameters of the kinematic transformation must be accurately known. Furthermore, the mathematical model for describing the kinematic transformation should be as complete as possible. Finally, the actual states of the adjusting elements must be exactly known.
The geometric parameters of the kinematic transformation comprise, inter alia, spatial coordinates of midpoints of links, and the mutual spacing of links. Such measurements are carried out as a rule on coordinate measuring machines. The parameters of the kinematic transformation, that is to say the positions of points of the basic member relative to one another, and the positions of points of the additional member relative to one another, can therefore be detected with sufficient accuracy as a rule. However, once these parameters have been detected, it is also still necessary to determine the actual states of the adjusting elements with high accuracy. This frequently constitutes a large problem in starting up a machine. The point is that in the overwhelming number of applications, it is necessary for the actual state to be exactly known in order to be able to adjust the additional member correctly. In the assembled state of the machine, however, the link midpoints are no longer accessible as a rule to direct measurement.
It is conceivable to set the actual states in repeated trials so that the positional accuracy of the additional member in the working space is as high as possible. However, this method is complicated and, moreover, not very accurate.
DE 198 28 181 A1 discloses a method for calibrating the kinematics. In this method, comparisons are made in the entire working space between a measured position and detected actual positions, and the parameters and the actual states of the adjusting elements are determined in such a way that the mean square error is minimized. This method also has only a limited accuracy and is, moreover, very complex mathematically.